The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A073491 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A073491

Numbers having no prime gaps in their factorization.
(history; published version)

#26 by N. J. A. Sloane at Fri Oct 02 22:08:20 EDT 2015

STATUS

proposed

approved

#25 by Jon E. Schoenfield at Fri Oct 02 21:52:56 EDT 2015

STATUS

editing

proposed

#24 by Jon E. Schoenfield at Fri Oct 02 21:52:54 EDT 2015

COMMENTS

The Heinz numbers of the partitions that have no gaps. The Heinz number of a partition p = [p_1, p_2, ..., p_r] is defined as Product_{j=1..r} (p_j-th prime, j=1...r) (concept used by _Alois P. Heinz _ in A215366 as an "encoding" of a partition). Example: (i) 18 (= 2*3*3) is in the sequence because it is the Heinz number of the partition [1,2,2]; (ii) 10 (= 2*5) is not in the sequence because it is the Heinz number of the partition [1,3]. - Emeric Deutsch, Oct 02 2015

STATUS

proposed

editing

#23 by Emeric Deutsch at Fri Oct 02 19:49:59 EDT 2015

STATUS

editing

proposed

#22 by Emeric Deutsch at Fri Oct 02 19:49:53 EDT 2015

COMMENTS

The Heinz numbers of the partitions that have no gaps. The Heinz number of a partition p = [p_1, p_2, ..., p_r] is defined as Product(p_j-th prime, j=1...r) (concept used by Alois P. Heinz in A215366 as an "encoding" of a partition). Example: (i) 18 (= 2*3*3) is in the sequence because it is the Heinz number of the partition [1,2,2]; (ii) 10 (= 2*5) is not in the sequence because it is the Heinz number of the partition [1,3]. - Emeric Deutsch, Oct 02 2015

STATUS

approved

editing

#21 by Charles R Greathouse IV at Tue Apr 28 17:10:31 EDT 2015

STATUS

editing

approved

#20 by Charles R Greathouse IV at Tue Apr 28 17:10:28 EDT 2015

COMMENTS

Essentially the same as A066311. [From _- _R. J. Mathar_, Sep 23 2008]

LINKS

T. D. Noe, <a href="/A073491/b073491.txt">Table of n, a(n) for n = 1..1000</a>

PROG

(PARI) is(n)=my(f=factor(n)[, 1]); for(i=2, #f, if(precprime(f[i]-1)>f[i-1], return(0))); 1 \\ Charles R Greathouse IV, Apr 28 2015

CROSSREFS

Cf. A137791, A137792, A137793, A137895.

Cf. A137895.

STATUS

approved

editing

#19 by Reinhard Zumkeller at Sat Dec 21 05:50:55 EST 2013

STATUS

editing

approved

#18 by Reinhard Zumkeller at Fri Dec 20 15:04:07 EST 2013

PROG

(Haskell)

a073491 n = a073491_list !! (n-1)

a073491_list = filter ((== 0) . a073490) [1..]

-- Reinhard Zumkeller, Dec 20 2013

STATUS

approved

editing

#17 by Charles R Greathouse IV at Thu Nov 21 13:11:39 EST 2013

MATHEMATICA

ok[n_] := (p = FactorInteger[n][[All, 1]]; PrimePi[Last@p] - PrimePi[First@p] == Length[p] - 1); Select[Range[135], ok] (* From _Jean-François Alcover, _, Apr 29 2011 *)

Discussion

Thu Nov 21

13:11

OEIS Server: https://oeis.org/edit/global/2066